Robustness of Kardar-Parisi-Zhang scaling in a classical integrable spin chain with broken integrability

Abstract

Recent investigations have observed superdiffusion in integrable classical and quantum spin chains. An intriguing connection between these spin chains and Kardar-Parisi-Zhang (KPZ) universality class has emerged. Theoretical developments (e.g. generalized hydrodynamics) have highlighted the role of integrability as well as spin-symmetry in KPZ behaviour. However understanding their precise role on superdiffusive transport still remains a challenging task. The widely used quantum spin chain platform comes with severe numerical limitations. To circumvent this barrier, we focus on a classical integrable spin chain which was shown to have deep analogy with the quantum spin-$\frac{1}{2}$ Heisenberg chain. Remarkably, we find that KPZ behaviour prevails even when one considers integrability-breaking but spin-symmetry preserving terms, strongly indicating that spin-symmetry plays a central role even in the non-perturbative regime. On the other hand, in the non-perturbative regime, we find that energy correlations exhibit clear diffusive behaviour. We also study the classical analog of out-of-time-ordered correlator (OTOC) and Lyapunov exponents. We find significant presence of chaos for the integrability-broken cases even though KPZ behaviour remains robust. The robustness of KPZ behaviour is demonstrated for a wide class of spin-symmetry preserving integrability-breaking terms.

10 pages, 9 figures (including supplementary material)

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Cited by in corpus (16)

• Dynamics of magnetization at infinite temperature in a Heisenberg spin chain
• Non-linear fluctuating hydrodynamics for KPZ scaling in isotropic spin chains
• Superdiffusion from nonabelian symmetries in nearly integrable systems
• Kardar-Parisi-Zhang scaling in the Hubbard model
• Spin diffusion in perturbed isotropic Heisenberg spin chain
• Slow crossover from superdiffusion to diffusion in isotropic spin chains
• Parametrically long lifetime of superdiffusion in non-integrable spin chains
• Efficient computation of cumulant evolution and full counting statistics: application to infinite temperature quantum spin chains
• KPZ fluctuations in finite volume
• Out-of-time-ordered correlator in the one-dimensional Kuramoto-Sivashinsky and Kardar-Parisi-Zhang equations
• Scaling of diffusion constants in perturbed easy-axis Heisenberg spin chains
• Ballistic conductance with and without disorder in a boundary-driven XXZ spin chain
• Lindblad quantum dynamics from correlation functions of classical spin chains
• A theory of quasiballistic spin transport
• Semiclassical analysis of spin dynamics in the non-Hermitian Hubbard model
• Nontrivial damping of magnetization currents in perturbed spin chains